def get_clebsch_hf_factors(self, F_level_idxs_a, F_level_idxs_b, q):
""" Returns a list of Clebsch-Gordan coefficients for the hyperfine
transition dipole matrix elements for each coupled level pair.
Args:
F_level_idx_a (int): F level the transition is from (lower level)
F_level_idx_b (int): F level the transition is to (upper level)
q (int): The field polarisation. Choose from [-1, 0, 1].
Returns:
(list): factors, length of mF_list
"""
# TODO: Selection rules? Either needs to be here or get_coupled_levels
mF_list = self.get_mF_list()
coupled_levels = self.get_coupled_levels(F_level_idxs_a,
F_level_idxs_b)
factors = np.empty(len(coupled_levels))
for i, cl in enumerate(coupled_levels):
a = mF_list[cl[0]]
b = mF_list[cl[1]]
factors[i] = calc_clebsch_hf(J_a=a['J'],
I_a=a['I'],
F_a=a['F'],
mF_a=a['mF'],
J_b=b['J'],
I_b=b['I'],
F_b=b['F'],
mF_b=b['mF'],
q=q)
return factors
def chf_17(F_b, mF_a): return angmom.calc_clebsch_hf(J_a=J_a, I_a=I_a,
F_a=2, mF_a=mF_a, J_b=J_b, I_b=I_b, F_b=F_b, mF_b=mF_a - 1, q=1)
self.assertAlmostEqual(chf_17(F_b=1, mF_a=-2), np.sqrt(0))
def test_Rb_87_5s12_5p12(self):
""" Testing Clebsch-Gordan coefficients for the Rb87 D1 line hyperfine
transitions. These coefficients are from Tables 15-20 in ref [1].
Notes:
[1]: Daniel A. Steck, 'Rubidium 87 D Line Data' available online
at http://steck.us/alkalidata. (revision 2.1.4, 23 Dec 2010).
"""
J_a = 1/2
J_b = 1/2
I_a = 3/2
I_b = 3/2
# Table 15
chf_15 = lambda F_b, mF_a: angmom.calc_clebsch_hf(J_a=J_a, I_a=I_a,
F_a=2, mF_a=mF_a, J_b=J_b, I_b=I_b, F_b=F_b, mF_b=mF_a + 1, q=-1)
self.assertAlmostEqual(chf_15(F_b=1, mF_a=-2), np.sqrt(1/2))
self.assertAlmostEqual(chf_15(F_b=1, mF_a=-1), np.sqrt(1/4))
self.assertAlmostEqual(chf_15(F_b=1, mF_a=0), np.sqrt(1/12))
self.assertAlmostEqual(chf_15(F_b=1, mF_a=1), np.sqrt(0))
self.assertAlmostEqual(chf_15(F_b=1, mF_a=2), np.sqrt(0))
self.assertAlmostEqual(chf_15(F_b=2, mF_a=-2), np.sqrt(1 / 6))
self.assertAlmostEqual(chf_15(F_b=2, mF_a=-1), np.sqrt(1 / 4))
self.assertAlmostEqual(chf_15(F_b=2, mF_a=0), np.sqrt(1 / 4))
self.assertAlmostEqual(chf_15(F_b=2, mF_a=1), np.sqrt(1/6))
self.assertAlmostEqual(chf_15(F_b=2, mF_a=2), np.sqrt(0))
# Table 16
chf_16 = lambda F_b, mF_a: angmom.calc_clebsch_hf(J_a=J_a, I_a=I_a,
F_a=2, mF_a=mF_a, J_b=J_b, I_b=I_b, F_b=F_b, mF_b=mF_a, q=0)
self.assertAlmostEqual(chf_16(F_b=1, mF_a=-2), np.sqrt(0))
self.assertAlmostEqual(chf_16(F_b=1, mF_a=-1), np.sqrt(1/4))
self.assertAlmostEqual(chf_16(F_b=1, mF_a=0), np.sqrt(1/3))
self.assertAlmostEqual(chf_16(F_b=1, mF_a=1), np.sqrt(1/4))
self.assertAlmostEqual(chf_16(F_b=1, mF_a=2), np.sqrt(0))
self.assertAlmostEqual(chf_16(F_b=2, mF_a=-2), -np.sqrt(1/3))
self.assertAlmostEqual(chf_16(F_b=2, mF_a=-1), -np.sqrt(1/12))
self.assertAlmostEqual(chf_16(F_b=2, mF_a=0), np.sqrt(0))
self.assertAlmostEqual(chf_16(F_b=2, mF_a=1), np.sqrt(1/12))
self.assertAlmostEqual(chf_16(F_b=2, mF_a=2), np.sqrt(1/3))
# Table 17
def chf_17(F_b, mF_a): return angmom.calc_clebsch_hf(J_a=J_a, I_a=I_a,
F_a=2, mF_a=mF_a, J_b=J_b, I_b=I_b, F_b=F_b, mF_b=mF_a - 1, q=1)
self.assertAlmostEqual(chf_17(F_b=1, mF_a=-2), np.sqrt(0))
self.assertAlmostEqual(chf_17(F_b=1, mF_a=-1), np.sqrt(0))
self.assertAlmostEqual(chf_17(F_b=1, mF_a=0), np.sqrt(1/12))
self.assertAlmostEqual(chf_17(F_b=1, mF_a=1), np.sqrt(1/4))
self.assertAlmostEqual(chf_17(F_b=1, mF_a=2), np.sqrt(1/2))
self.assertAlmostEqual(chf_17(F_b=2, mF_a=-2), np.sqrt(0))
self.assertAlmostEqual(chf_17(F_b=2, mF_a=-1), -np.sqrt(1/6))
self.assertAlmostEqual(chf_17(F_b=2, mF_a=0), -np.sqrt(1/4))
self.assertAlmostEqual(chf_17(F_b=2, mF_a=1), -np.sqrt(1/4))
self.assertAlmostEqual(chf_17(F_b=2, mF_a=2), -np.sqrt(1/6))
# Table 18
chf_18 = lambda F_b, mF_a: angmom.calc_clebsch_hf(J_a=J_a, I_a=I_a,
F_a=1, mF_a=mF_a, J_b=J_b, I_b=I_b, F_b=F_b, mF_b=mF_a+1, q=-1)
self.assertAlmostEqual(chf_18(F_b=1, mF_a=-1), -np.sqrt(1/12))
self.assertAlmostEqual(chf_18(F_b=1, mF_a=0), -np.sqrt(1/12))
self.assertAlmostEqual(chf_18(F_b=1, mF_a=1), np.sqrt(0))
self.assertAlmostEqual(chf_18(F_b=2, mF_a=-1), -np.sqrt(1/12))
self.assertAlmostEqual(chf_18(F_b=2, mF_a=0), -np.sqrt(1/4))
self.assertAlmostEqual(chf_18(F_b=2, mF_a=1), -np.sqrt(1/2))
# Table 19
chf_19 = lambda F_b, mF_a: angmom.calc_clebsch_hf(J_a=J_a, I_a=I_a,
F_a=1, mF_a=mF_a, J_b=J_b, I_b=I_b, F_b=F_b, mF_b=mF_a, q=0)
self.assertAlmostEqual(chf_19(F_b=1, mF_a=-1), np.sqrt(1/12))
self.assertAlmostEqual(chf_19(F_b=1, mF_a=0), np.sqrt(0))
self.assertAlmostEqual(chf_19(F_b=1, mF_a=1), -np.sqrt(1/12))
self.assertAlmostEqual(chf_19(F_b=2, mF_a=-1), np.sqrt(1/4))
self.assertAlmostEqual(chf_19(F_b=2, mF_a=0), np.sqrt(1/3))
self.assertAlmostEqual(chf_19(F_b=2, mF_a=1), np.sqrt(1/4))
# Table 20
def chf_20(F_b, mF_a): return angmom.calc_clebsch_hf(J_a=J_a, I_a=I_a,
F_a=1, mF_a=mF_a, J_b=J_b, I_b=I_b, F_b=F_b, mF_b=mF_a - 1, q=1)
self.assertAlmostEqual(chf_20(F_b=1, mF_a=-1), np.sqrt(0))
self.assertAlmostEqual(chf_20(F_b=1, mF_a=0), np.sqrt(1 / 12))
self.assertAlmostEqual(chf_20(F_b=1, mF_a=1), np.sqrt(1 / 12))
self.assertAlmostEqual(chf_20(F_b=2, mF_a=-1), -np.sqrt(1 / 2))
self.assertAlmostEqual(chf_20(F_b=2, mF_a=0), -np.sqrt(1 / 4))
self.assertAlmostEqual(chf_20(F_b=2, mF_a=1), -np.sqrt(1 / 12))